x ≤ 12
Solution:
Let us take the number be x.
A number : x
A number divided by three : 
A number divided by three less two : 
A number divided by three less two is at most two : 
Now, simplify the inequality,
Add 2 on both sides of the inequality,
Multiply by 3 on both sides of the equation,
Hence x ≤ 12.
Step-by-step explanation:
We are asked to simply (2√5 + 3√2)². Using formula: (a + b)² = a² + b² + 2ab. Let's say 2√5 = a, 3√2 = b. So,
→ (a + b)² = a² + b² + 2ab
→ (2√5 + 3√2)² = (2√5)² + (3√2)² + 2(2√5)(3√2)
We are aware about the fact that root means 1/2 and square of root means 2/2 that is 1. Using this we get:
→ (2√5 + 3√2)² = 4(5) + 9(2) + 2(2√5)(3√2)
Solve the brackets, to do so first put the like terms in one box.
→ (2√5 + 3√2)² = 4(5) + 9(2) + 2(2*3)(√5)(√2)
Solve the rest calculations.
→ (2√5 + 3√2)² = 20 + 18 + 2(6)(√10)
→ (2√5 + 3√2)² = 38 + 12√10
Option (a) (38 + 12√10) is the correct option.
It took them 4 days to install 480 chairs which means if they were working at a constant rate they got 120 chairs installed daily. with 360 chairs left that means in 3 days they will finish. so overall, it took the workers 7 days to finish, or a week.
vertex = (3,- 5 )
given a quadratic in standard form : y = ax² + bx + c ( a ≠ 0 ), then
the x-coordinate of the vertex is
= - 
y = x² - 6x + 4 is in standard form
with a = 1, b = - 6 and c = 4, hence
= - 
= 3
substitute this value into the equation for y- coordinate
y = 3² - 6(3) + 4 = 9 - 18 + 4 = - 5
vertex = (3, - 5 ) → second table
Answer:
Step-by-step explanation:
Begin the solution by squaring both sides of the given equation. We get:
(3x - 4)^2 = 2x^2 - 2x + 2, or:
9x^2 - 24x + 16 = 2x ^2 - 2x + 2
Combining like terms results in:
7x^2 - 22x + 14 = 0
and the coefficients are a = 7, b = -22, c = 14, so that the discriminant of the quadratic formula, b^2 - 4ac becomes (-22)^2 - 4(7)(14) = 92
According to the quadratic formula, the solutions are
-b ± √discriminant -(-22) ± √92 22 ± √92
x = ------------------------------- = ----------------------- = ------------------------
2a 14 14
